With a 6s or SE or higher you can shoot DNG as well and compare to what Apple spits out of their image processor. I played around in Lightroom for a little bit and the differences were definitely there.
Lightroom Mobile is my current weapon of choice for this, also provides a basic processing interface + sync with Adobe CC so you can grab them from your desktop. There's plenty of others out there, but since I already have a CC subscription I just went with it (as it does require you have at minimum Lightroom CC).